The guiding of optical radiation by waveguides such as planar waveguides or optical fibres is well known. While planar waveguides have a wide range of structures and geometries, as illustrated in FIGS. 2a to 2f, optical fibres, as shown in FIG. 3, usually have a circular transverse cross-section. FIGS. 2a to 2f show a sample of classical “simple” planar waveguide geometries; more complex variations of these are widely used to perform integrated optical functions such as coupling and switching. Optical waveguides rely on total internal reflection at an interface between two media of different refractive index to confine light within their cores. A wide range of materials from silica to polymers have been used to manufacture optical waveguides providing a range of properties.
Referring to the cross-section of a planar optical waveguide in FIG. 1, the general structure of a planar optical waveguide 10 comprises a core 11 of refractive index nc on a substrate 12 of refractive index ns, the core being enclosed by one or more layers of cladding 13, 14 of a lower refractive index nR, nL than that of the core, i.e. ns, nR, nL<nc. Under appropriate circumstances, mainly due to the difference in refractive indices, light injected into the core 11 at a first end of the optical waveguide 10 is confined to propagate along the core and is emitted at a second end of the optical waveguide 10, opposed to the first end.
Depending on the geometry and material composition of an optical waveguide, the emitted light will have different properties from the light that was injected into the optical waveguide. Intensity, spectral distribution and the polarization state of a wave are generally voluntarily or involuntarily modified by propagation through the waveguide.
Optical fibres are the most commonly used optical waveguides. Because of their low attenuation and compactness, and because they are not affected by electromagnetic field variations in a surrounding environment, optical fibres are used to transport light signals over very long distances without repeating electronics, to transport large numbers of signals simultaneously over short and medium distances without interference and to make sensors of many kinds, such as strain and temperature sensors.
Referring to FIG. 3, an optical fibre 30 is generally formed of a single core 31 of circular transverse cross-section, covered by a concentric cladding 33 with a refractive index slightly lower than a refractive index of the core 31. A typical near infrared multimode fibre has a 50 μm diameter core of Ge-doped silica with a refractive index n1 and a 125 μm diameter cladding of undoped silica, refractive index n2=1.46. A typical refractive index difference (n1-n2) is in the range 0.001 to 0.01. The cladding 33 may be covered by a protective layer 35.
In a monomode optical fibre light propagates in a single mode. In a multimode optical fibre, light propagates at a given wavelength in a finite, discrete number of optical modes. It is generally difficult to provide a mathematical expression for every propagating mode when a fibre is multimode. Nevertheless, it is possible to provide an approximate number of the modes. It is also possible to predict some characteristics such as a speed of propagation of a pulse, its attenuation and the broadening the pulse suffers through propagation.
A very useful parameter to describe an optical fibre is its Numerical Aperture (NA) which defines an acceptance angle θ of the fibre according to:NA=n1 sin θ
Extending the analysis, the following expression for the Numerical Aperture is obtained:NA=√{square root over (n12−n22)}Thus this parameter depends on only the core and cladding refractive indexes. Any light entering at an angle of incidence greater than the acceptance angle θ will be dissipated in the cladding and protective layer.
Knowing the numerical aperture, one can calculate a normalized frequency V for the propagation, where a is the core radius and k0 a propagation vector:V=ak0NA
For a step index fibre, a single mode (LP01) is guided when 1<V<2.405
For V>>1 the number N of modes propagating through the fibre at the given wavelength is given approximately by
  N  ≈            V      2        2  
It can be shown that each guided mode traveling through a multimode fibre has a slightly different speed. This phenomenon is known as intermodal dispersion and normally causes a serious limitation to the bandwidth of an optical fibre. An optical pulse injected into the fibre is broadened with distance by the intermodal dispersion. If not taken into account, this phenomenon prevents resolution of successive pulses.
A propagation constant βm for a guided mode m, at wavelength λ0 can be shown to meet the condition:k02n22<βm2<k02n12 
Disregarding both guide and material dispersion, which are usually much smaller than intermodal dispersion, one can show that the intermodal dispersion D can be written as:
  D  ≅            NA      2              2      ⁢              n        1            ⁢      c      
As a consequence, a maximum delay between the “fastest” and the “slowest” mode over a distance L can be expressed as:
      Δ    ⁢                  ⁢    τ    ≅                    NA        2                    2        ⁢                  n          1                ⁢        c              ⁢    L  
A coherence time is generally defined as an average duration of a wave train, i.e. a time for the wave train to travel a coherence length L. One manifestation of the coherence time is a fringe contrast variation obtained when lengthening a reference arm in a Michelson-like interferometric setup, as shown in FIG. 4.
WO 2007/072335 discloses a multimode waveguide in combination with an oscillating mirror for reducing the visibility of speckle to the human eye, the period of the mirror being below the integration time of the eye. A light modulation panel receives light transmitted from the mirror through the multimode optical fibre and modulates an intensity per pixel of the image. A projection lens projects an image from the light modulation panel onto a screen, with angular scanning by the oscillating mirror retained thereon. In a second embodiment disclosed in WO 2007/072335, the multimode optical fibre is located between the laser source and the oscillating mirror instead of between the oscillating mirror and the light modulation panel.